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Portfolio Optimization Based on Expected Shortfall
Appendix A ClosedForm Formulas of Estimation Errors
asymptotic Bloomberg L.P. calculated Call option closed-form formula component expected shortfall conditional expectation Confidence Interval 95 correlation coefficient data window Decomposing Expected Shortfall decomposition default rate distribution function distribution is fat-tailed efficient frontier Electric stock error of expected estimation error example of decomposing expected shortfall estimates Hiroshi Fujiki individual risk factor Inflation Intel stock Kunio Okina log returns marginal expected shortfall McDonald's stock method of decomposing Monetary Policy Monte Carlo simulations Naohiko Baba normal distribution obtain option on Intel option on McDonald's Pareto Pareto distribution Portfolio confidence level portfolio in Section portfolio loss Portfolio Optimization Based probability density function random variable Relative Standard Deviation Risk Measures Deviation Rockafeller and Uryasev Sample Loan Portfolio sample option portfolio sample portfolio Shigenori Shiratsuka shortfall is larger Shortfall of Sample simulation-based stable distribution Standard Deviation Confidence Standard Relative Standard stock 18 strike prices sub-additive Table Tasche Theorem Toshinao Yoshiba underlying loss distribution US$/unit variance-covariance matrix